Consider a rigid body rotating about a fixed z-axis. Let the position vector of i-th particle be
ri and its linear momentum be
pi. Its angular momentum about the origin is denoted by

In general, for a rigid body rotating about a fixed axis, its angular momentum L does not lie along the axis of rotation. It can be shown that for a rigid body that is symmetrical about the axis of rotation, the angular momentum is along its axis of rotation.

If the external torque is zero, then

Therefore, we get L
z or Iω as constant. This is the Law of Conservation of Angular Momentum pertaining to rotation about a fixed axis. It states that in the absence of net external torque, the total angular momentum of the system remains conserved.

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